Firm arch support features a strong compression band through the midfoot of the sock, giving you maximum stability and a locked-in feel inside your boot. It's a great choice if you have high arches, struggle with foot fatigue during long days on the mountain, or want every bit of performance and sock stability you can get.
That said, firm support isn't for everyone. If you have flat feet or prefer a less restrictive feel, it can feel uncomfortable or even distracting. It's also worth remembering that sock arch support is different from your boot footbed or insole — the sock's compression keeps the sock itself from slipping and bunching, while your insole supports your actual foot.
If you're skiing hard all day and your arches are begging for help by afternoon, firm arch support is worth trying. Otherwise, moderate support is a safer, more comfortable bet for most skiers.